Android 4.2.2 is an older operating system, and many apps have stopped receiving security updates for it. For a safer experience, using the mobile browser is highly recommended over installing unverified third-party APKs.
Search for or earlier (supports Android 4.1–4.4). Recommended sources (always scan with antivirus):
While unlikely for the main app, you should still check the Google Play Store first. If a compatible legacy version is available for your specific hardware, the "Install" button will appear.
To get it, search for "Facebook Lite APK old version" on the mirror sites mentioned above. Download and install it just as you would the main app. For many users on Android 4.2.2, this is actually the superior experience.
This is the tricky part. You need a version of Facebook that was built for Android 4.2.2 but is new enough to still function. Generally, versions ranging from the late 50.x series to the early 100.x series (e.g., v60.0.0.0) work best on Jelly Bean.